题目要求

Given a stack which can keep M numbers at most. Push N numbers in the order of 1, 2, 3, ..., N and pop randomly. You are supposed to tell if a given sequence of numbers is a possible pop sequence of the stack. For example, if M is 5 and N is 7, we can obtain 1, 2, 3, 4, 5, 6, 7 from the stack, but not 3, 2, 1, 7, 5, 6, 4.

Input Specification:

Each input file contains one test case. For each case, the first line contains 3 numbers (all no more than 1000): M (the maximum capacity of the stack), N (the length of push sequence), and K (the number of pop sequences to be checked). Then K lines follow, each contains a pop sequence of N numbers. All the numbers in a line are separated by a space.

Output Specification:

For each pop sequence, print in one line "YES" if it is indeed a possible pop sequence of the stack, or "NO" if not.

Sample Input:

5 7 5
1 2 3 4 5 6 7
3 2 1 7 5 6 4
7 6 5 4 3 2 1
5 6 4 3 7 2 1
1 7 6 5 4 3 2

Sample Output:

YES
NO
NO
YES
NO

解题思路

本题主要使用了STL中的栈(stack)来模拟一个栈进行操作。

使用cur记录当前应该入栈的元素,依次读取pop sequence中的元素,对于每个读取到的元素,主要遵循以下几个原则:

  1. 如果要输出的元素正好是当前栈顶的元素,则栈顶出栈
  2. 如果要输出的元素大于等于cur,则将[cur, 要输出元素]这一区间内的元素全部入栈,然后出栈一次。出栈前判断栈是否溢出,如果溢出,则直接输出NO
  3. 如果要输出的元素小于cur,并且栈顶不是该元素(出栈得到的不是目的元素),则直接输出NO

一个pop sequence里的元素全部读取处理完毕,并且没有出现错误,则输出YES。

代码

#include <cstdio>
#include <cstdlib>
#include <stack>

using namespace std;

int main()
{
    int num;
    int m, n, k;
    scanf("%d%d%d", &m, &n, &k);
    bool ok = true;
    for (int i = 0; i < k; i++)
    {
        stack<int> s;
        int cur = 1;
        ok = true;
        for (int j = 0; j < n; j++)
        {
            scanf("%d", &num);
            if (!ok)
            {
                continue;
            }
            if (!s.empty() && num == s.top())
            {
                s.pop();
            }
            else if (num < cur && num != s.top())
            {
                printf("NO\n");
                ok = false;
            }
            else
            {
                while (cur <= num)
                {
                    s.push(cur);
                    cur++;
                }
                if (s.size() > m)
                {
                    printf("NO\n");
                    ok = false;
                }
                s.pop();
            }
        }
        if (ok)
        {
            printf("YES\n");
        }
    }

    system("pause");
    return 0;
}